iron emission lines 3) Iron Emission Lines (25 points) a. According to the Bohr

Question

iron emission lines

3) Iron Emission Lines (25 points) a. According to the Bohr model, whatenergy of a photon emitted as an electron falls from the n- 2 to the n 1 state o charge Z of Fe is 26. You may neglect the influence of the other electrons outside the ground state. Give your answer in keV. What part of the spectrum does this lie in? on (Fe) atom? Recall that the nuclear b. According to the Bohr model, what is the speed of the electron in the ground state n-1 of Fe? Give your answer in terms of the speed of light. c. Using part b, estimate the magnitude of the relativistic correction to the ground state of Fe by computing the ratio of the relativistic kinetic energy to the non-relativistic kinetic energy. Recall that you showed on the homework that the leading-order relativistic kinetic energy is (3/8)mue

Explanation / Answer

part a:

energy level for n=-13.6*Z^2/n^2. eV

so energy of photon released when electron falls from =2 to n=1:

(-13.6*26^2/2^2)-(-13.6*26^2/1^2)

=6895.2 eV

=6.8952 keV

it falls in x ray level.

part b:

energy for ground state=n=1 is given by

13.6*26^2/1^2=9193.6 eV

=1.471*10^(-15) J

then speed=sqrt(2*energy/mass of electron)

=5.686*10^7 m/s

part c:

ratio=1/sqrt(1-(v/c)^2)=1.0185

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